Washington ? Consumer prices advanced in May at the fastest pace in more than three years, as rapidly increasing food and fuel costs forced Americans to dig deeper into their pockets.

But even with the pickup, Federal Reserve Chairman Alan Greenspan said Tuesday that he and his Fed colleagues weren’t worried that the country was on the brink of an unwanted surge in inflation. Any interest rate increases by the Fed would be at a measured pace unless economic conditions change, he said.

The Consumer Price Index, the government’s most closely watched inflation barometer, rose 0.6 percent last month, the largest increase since January 2001 and up from a 0.2 percent rise in April, the Labor Department reported.

However, the “core” rate of inflation, which excludes volatile food and energy prices, increased by only 0.2 percent in May, down from a 0.3 percent rise the month before. From an economic point of view, that suggested prices of other goods and services were more subdued — an encouraging sign that inflation is not a danger to the economy, analysts said.

Nonetheless, the latest snapshot of the nation’s inflation climate would justify a move by the Federal Reserve to raise interest rates for the first time in four years when it meets later this month, economists said.

Appearing at a Senate hearing on his nomination to a fifth term as Fed chief, Greenspan said he and his colleagues still hold the view that “inflationary pressures are not likely to be a serious concern in the period ahead” and they probably can boost interest rates gradually to head off inflation. If their forecasts, however, turn out to be wrong, Greenspan again suggested, as he did last week, that more aggressive action could be taken.